Siegel measures

The goals of this paper are first to describe and then to apply an ergodic-theoretic generalization of the Siegel integral formula from the geometry of numbers. The general formula will be seen to serve both as a guide and as a tool for questions concerning the distribution, in senses to be made precise, of the set of closed leaves of measured foliations subordinate to meromorphic quadratic differentials on closed Riemann surfaces.Comment: 50 pages, published versio

Geodesic laminations revisited

The Bratteli diagram is an infinite graph which reflects the structure of projections in a C*-algebra. We prove that every strictly ergodic unimodular Bratteli diagram of rank 2g+m-1 gives rise to a minimal geodesic lamination with the m-component principal region on a surface of genus g greater or equal to 1. The proof is based on the Morse theory of the recurrent geodesics on the hyperbolic surfaces.Comment: 13 pages, 2 figures, revised versio

Parity of the spin structure defined by a quadratic differential

According to the work of Kontsevich-Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities,is the parity of the spin structure. We show that for the moduli space of quadratic differentials, the spin structure is constant on every stratum where it is defined. In particular this disproves the conjecture that it classifies the non-hyperelliptic connected components of the strata of quadratic differentials with prescribed singularities. An explicit formula for the parity of the spin structure is given.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper12.abs.htm

Considering Colonoware from the Barnes Plantation: A Proposed Colonoware Typology for Northern Virginia Colonial Sites

Colonoware vessels and vessel fragments have been recovered from numerous colonial and antebellum sites in Virginia, and the number of newly reported sites increases with each excavation season. What this growing corpus of Virginia colonoware presently requires, however, is an adequate, standardized typology for pottery classification, at both site-specific and regional scales. Here, the colonoware typology designed during analysis of collections from the Barnes Plantation (44FX1326), a mid-18th century tobacco plantation in Fairfax County, Virginia, is explained and offered for use elsewhere. Colonware sherds from contemporaneous northern Virginia plantation sites exhibit many of the same charcteristics as those found at the Barnes site, and thus the typology holds promise for region-wide use

On embedding of the Bratteli diagram into a surface

We study C*-algebras O_{\lambda} which arise in dynamics of the interval exchange transformations and measured foliations on compact surfaces. Using Koebe-Morse coding of geodesic lines, we establish a bijection between Bratteli diagrams of such algebras and measured foliations. This approach allows us to apply K-theory of operator algebras to prove strict ergodicity criterion and Keane's conjecture for the interval exchange transformations.Comment: final versio

Triangulations and volume form on moduli spaces of flat surfaces

In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, we define a volume form on this moduli space, and show that, in the well-known cases, this volume form agrees with usual ones, up to a multiplicative constant.Comment: 42 page

Connecting geodesics and security of configurations in compact locally symmetric spaces

A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure

Foliations on modular curves

It is proved, that a foliation on a modular curve given by the vertical trajectories of holomorphic differential corresponding to the Hecke eigenform is either the Strebel foliation or the pseudo-Anosov foliation.Comment: to appear Bulletin of the Brazilian Mathematical Society, New Serie

OncoLog Volume 54, Number 6, June 2009

Chronic Myelogenous Leukemia: Refining Approaches to Treatment Advancing the Treatment of Lymphedema House Call: Hospice: Comforting Care When the End Is Nearhttps://openworks.mdanderson.org/oncolog/1196/thumbnail.jp

OncoLog Volume 53, Number 09, September 2008

Deciphering Metastatic Colorectal Carcinoma House Call: Planning Ahead with Advance Directives A Child-Centered Approach to Anesthesia for Proton Therapyhttps://openworks.mdanderson.org/oncolog/1173/thumbnail.jp